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Popular >

derivative of ln(((1-x)/(1+x)))

Solution

\frac{d}{d x} (ln (\frac{( 1 - x )}{1 + x}))

Solution

- \frac{2}{( - x + 1 ) ( x + 1 )}

Solution steps

\frac{d}{d x} (ln (\frac{( 1 - x )}{1 + x}))

Apply the chain rule:

\frac{1}{\frac{1 - x}{1 + x}} \frac{d}{d x} (\frac{1 - x}{1 + x})

= \frac{1}{\frac{1 - x}{1 + x}} \frac{d}{d x} (\frac{1 - x}{1 + x})

\frac{d}{d x} (\frac{1 - x}{1 + x}) = - \frac{2}{( 1 + x ) ^{2}}

= \frac{1}{\frac{1 - x}{1 + x}} (- \frac{2}{( 1 + x ) ^{2}})

Simplify

\frac{1}{\frac{1 - x}{1 + x}} (- \frac{2}{( 1 + x ) ^{2}}) : - \frac{2}{( - x + 1 ) ( x + 1 )}

= - \frac{2}{( - x + 1 ) ( x + 1 )}

Popular Examples

integral from 1 to 9 of pi(sqrt(x-1))^2

\int_{1}^{9} π (x - 1)^{2} d x

limit as s approaches 0 of 3/(s*(s+2))

s \to 0 lim (\frac{3}{s \cdot ( s + 2 )})

derivative of (x^3)/9 derivative of

\frac{x ^{3}}{9}

(sin(xy)+xycos(xy))dx+(x^2cos(xy))dy=0

(sin (x y) + x y cos (x y)) d x + (x^{2} cos (x y)) d y = 0

limit as x approaches 2+of (x^2+1)/(x-2)

x \to 2 + lim (\frac{x ^{2} + 1}{x - 2})

Frequently Asked Questions (FAQ)

What is the derivative of ln(((1-x)/(1+x))) ?
The derivative of ln(((1-x)/(1+x))) is -2/((-x+1)(x+1))
What is the first derivative of ln(((1-x)/(1+x))) ?
The first derivative of ln(((1-x)/(1+x))) is -2/((-x+1)(x+1))